Lastly, for commuting pairs \(L\) , \(M\) , it is easy to observe the existence of a polynomial \(h(\lambda ,\mu )\)  with constant coefficients such that,
identically in the independent variable, \(h(L,M)=0\) : Burchnall and Chaundy showed that the opposite is also true [1]}, [2]}. This is the defining polynomial of a plane curve, commonly known as spectral curve \(\Gamma \) , and it can be computed by means of the differential resultant of \(L-\lambda \)  and \(M-\mu \) . Furthermore for a true rank \(r\)  pair we have
\(\partial {\rm Res}(L-\lambda ,M-\mu )=h(\lambda ,\mu )^r,\) 
